Synopsis Based on the research experience of the author complex variable with Vector Calculus provides clear and condensed treatment of the subject. This book should be used by undergraduate students of engineering and science as a part of a course in Advanced Engineering Mathematics, where they are introduced to complex variables, through conceptual development of analysis. This book also presents a detailed treatment of vector calculus and its applications. This book also introduces vector algebra, step by step, with due emphasis on various operations on vector field and scalar fields. There are many examples are given in this book in order to clarify the ideas and familiarize students with various techniques of problem solving.